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 A123963 Triangle T(n, k) = k^4 - n^4 + 2*k*n*(1 - k^2*n^2), read by rows. 1
 0, -1, 0, -16, -27, -120, -81, -128, -485, -1440, -256, -375, -1248, -3607, -8160, -625, -864, -2589, -7264, -16329, -31200, -1296, -1715, -4712, -12843, -28640, -54611, -93240, -2401, -3072, -7845, -20800, -45993, -87456, -149197, -235200, -4096, -5103, -12240, -31615, -69312, -131391, -223888, -352815, -524160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A triangular sequence based on the omega(3) Jacobian Elliptic Modular equation. LINKS G. C. Greubel, Rows n = 0..100 of the triangle, flattened Eric Weisstein's World of Mathematics, Modular Equation FORMULA T(n, k) = k^4 - n^4 + 2*k*n*(1 - k^2*n^2). Sum_{k=0..n} T(n, k) = (-1/15)*binomial(n+1, 2) * (15*n^5 +15*n^4 +24*n^3 -9*n^2 -31*n +1). - G. C. Greubel, Feb 20 2021 EXAMPLE Triangular sequence:       0;      -1,     0;     -16,   -27,   -120;     -81,  -128,   -485,  -1440;    -256,  -375,  -1248,  -3607,  -8160;    -625,  -864,  -2589,  -7264, -16329,  -31200;   -1296, -1715,  -4712, -12843, -28640,  -54611,  -93240;   -2401, -3072,  -7845, -20800, -45993,  -87456, -149197, -235200;   -4096, -5103, -12240, -31615, -69312, -131391, -223888, -352815, -524160; MATHEMATICA T[n_, k_]:= k^4 - n^4 + 2*n*k*(1 - k^2*n^2); Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Feb 20 2021 *) PROG (Sage) flatten([[k^4 - n^4 + 2*n*k*(1 - k^2*n^2) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 20 2021 (Magma) [k^4 - n^4 + 2*n*k*(1 - k^2*n^2): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 20 2021 CROSSREFS Sequence in context: A329206 A280935 A067650 * A073396 A338093 A302553 Adjacent sequences:  A123960 A123961 A123962 * A123964 A123965 A123966 KEYWORD sign AUTHOR Roger L. Bagula, Oct 28 2006 EXTENSIONS Edited by G. C. Greubel, Feb 20 2021 STATUS approved

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)